Abstract
We answer to a problem raised by recent work of Jelonek and Kurdyka: how can one detect by rational arcs the bifurcation locus of a polynomial map \({\mathbb {R}}^n\rightarrow {\mathbb {R}}^p\) in case \(p>1\). We describe an effective estimation of the “non-trivial” part of the bifurcation locus.
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Notes
We thank Y. Chen for suggesting us to test this example.
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Acknowledgments
LRGD acknowledges support from the Fapemig-Proc APQ-00431-14 Grant. ST acknowledges support from MPIM, Bonn. LRGD and MT acknowledge support from the USP-COFECUB Uc Ma 133/12 Grant. ST and MT acknowledge support from the CNRS-Tubitak No. 25784 Grant, from Université de Lille 1 and from Labex CEMPI (ANR-11-LABX-0007-01). The authors thank the anonymous referees for their valuable suggestions.
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Communicated by Teresa Krick.
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Dias, L.R.G., Tanabé, S. & Tibăr, M. Toward Effective Detection of the Bifurcation Locus of Real Polynomial Maps. Found Comput Math 17, 837–849 (2017). https://doi.org/10.1007/s10208-016-9303-2
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DOI: https://doi.org/10.1007/s10208-016-9303-2